Convergence and continuity criteria for discrete approximations of the continuous planar skeleton
CVGIP: Image Understanding
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The Medial axis of a union of balls
Computational Geometry: Theory and Applications
Any open bounded subset of Rn has the same homotopy type than its medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Medial axis approximation from inner Voronoi balls: a demo of the Mesecina tool
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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Consider a dense sampling S of the smooth boundary of a planar shape O, i.e., an open subset of R^2. We show that the medial axis of the union of Voronoi balls centered at Voronoi vertices inside O has a particularly simple structure: it is the union of all Voronoi vertices inside O and the Voronoi edges connecting them. Therefore, the medial axis of the union of these inner balls can be computed more efficiently and robustly than for a general union of balls. Our algorithm requires only the computation of a single Delaunay triangulation which is of complexity O(nlogn), whereas the general algorithm needs two Delaunay triangulations and a power diagram of quadratic complexity in the number of inner Voronoi balls. Also, our solution yields robust results even without using exact arithmetic, because it avoids the computation of the power diagram of the inner Voronoi balls whose configuration is highly degenerate.